http://revach.net/article.php?id=250

Section: Halacha   Category: Tshuvos
Shavuos Temimos: Do We Need to Wait for Tzais Hacochavim For Maariv Shavuos Night?

Although the Mishna Berura (494:1) brings the Taz who says that we do not daven Maariv before Tzais on Shavuos because we need our Sefiras HaOmer to be "Temimos" complete, the Magen Avrohom and the Shla Hakadosh both hold that this applies only to Kiddush and eating and not Maariv. Rav Yaakov Emden goes even further and says that it is a mitzva to daven Maariv early to be "Mosif MiChol Al Hakodesh" but also agrees that one should not make Kiddush or eat.

We are noheg not to daven Maariv early and the Piskei Tshuvos brings two possible reasons for this minhag. First, because we may end up eating early if we daven early. Second, because we may forget to say Krias Shema again after Tzais, since we don't sleep Shavuos and we won't at least say Krias Shema Al HaMitah.